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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    package org.apache.commons.math3.stat.clustering;<a name="line.17"></a>
<FONT color="green">018</FONT>    <a name="line.18"></a>
<FONT color="green">019</FONT>    import java.util.ArrayList;<a name="line.19"></a>
<FONT color="green">020</FONT>    import java.util.Collection;<a name="line.20"></a>
<FONT color="green">021</FONT>    import java.util.HashMap;<a name="line.21"></a>
<FONT color="green">022</FONT>    import java.util.HashSet;<a name="line.22"></a>
<FONT color="green">023</FONT>    import java.util.List;<a name="line.23"></a>
<FONT color="green">024</FONT>    import java.util.Map;<a name="line.24"></a>
<FONT color="green">025</FONT>    import java.util.Set;<a name="line.25"></a>
<FONT color="green">026</FONT>    <a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.exception.NotPositiveException;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.exception.NullArgumentException;<a name="line.28"></a>
<FONT color="green">029</FONT>    import org.apache.commons.math3.util.MathUtils;<a name="line.29"></a>
<FONT color="green">030</FONT>    <a name="line.30"></a>
<FONT color="green">031</FONT>    /**<a name="line.31"></a>
<FONT color="green">032</FONT>     * DBSCAN (density-based spatial clustering of applications with noise) algorithm.<a name="line.32"></a>
<FONT color="green">033</FONT>     * &lt;p&gt;<a name="line.33"></a>
<FONT color="green">034</FONT>     * The DBSCAN algorithm forms clusters based on the idea of density connectivity, i.e.<a name="line.34"></a>
<FONT color="green">035</FONT>     * a point p is density connected to another point q, if there exists a chain of<a name="line.35"></a>
<FONT color="green">036</FONT>     * points p&lt;sub&gt;i&lt;/sub&gt;, with i = 1 .. n and p&lt;sub&gt;1&lt;/sub&gt; = p and p&lt;sub&gt;n&lt;/sub&gt; = q,<a name="line.36"></a>
<FONT color="green">037</FONT>     * such that each pair &amp;lt;p&lt;sub&gt;i&lt;/sub&gt;, p&lt;sub&gt;i+1&lt;/sub&gt;&amp;gt; is directly density-reachable.<a name="line.37"></a>
<FONT color="green">038</FONT>     * A point q is directly density-reachable from point p if it is in the &amp;epsilon;-neighborhood<a name="line.38"></a>
<FONT color="green">039</FONT>     * of this point.<a name="line.39"></a>
<FONT color="green">040</FONT>     * &lt;p&gt;<a name="line.40"></a>
<FONT color="green">041</FONT>     * Any point that is not density-reachable from a formed cluster is treated as noise, and<a name="line.41"></a>
<FONT color="green">042</FONT>     * will thus not be present in the result.<a name="line.42"></a>
<FONT color="green">043</FONT>     * &lt;p&gt;<a name="line.43"></a>
<FONT color="green">044</FONT>     * The algorithm requires two parameters:<a name="line.44"></a>
<FONT color="green">045</FONT>     * &lt;ul&gt;<a name="line.45"></a>
<FONT color="green">046</FONT>     *   &lt;li&gt;eps: the distance that defines the &amp;epsilon;-neighborhood of a point<a name="line.46"></a>
<FONT color="green">047</FONT>     *   &lt;li&gt;minPoints: the minimum number of density-connected points required to form a cluster<a name="line.47"></a>
<FONT color="green">048</FONT>     * &lt;/ul&gt;<a name="line.48"></a>
<FONT color="green">049</FONT>     * &lt;p&gt;<a name="line.49"></a>
<FONT color="green">050</FONT>     * &lt;b&gt;Note:&lt;/b&gt; as DBSCAN is not a centroid-based clustering algorithm, the resulting<a name="line.50"></a>
<FONT color="green">051</FONT>     * {@link Cluster} objects will have no defined center, i.e. {@link Cluster#getCenter()} will<a name="line.51"></a>
<FONT color="green">052</FONT>     * return {@code null}.<a name="line.52"></a>
<FONT color="green">053</FONT>     *<a name="line.53"></a>
<FONT color="green">054</FONT>     * @param &lt;T&gt; type of the points to cluster<a name="line.54"></a>
<FONT color="green">055</FONT>     * @see &lt;a href="http://en.wikipedia.org/wiki/DBSCAN"&gt;DBSCAN (wikipedia)&lt;/a&gt;<a name="line.55"></a>
<FONT color="green">056</FONT>     * @see &lt;a href="http://www.dbs.ifi.lmu.de/Publikationen/Papers/KDD-96.final.frame.pdf"&gt;<a name="line.56"></a>
<FONT color="green">057</FONT>     * A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise&lt;/a&gt;<a name="line.57"></a>
<FONT color="green">058</FONT>     * @version $Id: DBSCANClusterer.java 1410882 2012-11-18 12:49:49Z tn $<a name="line.58"></a>
<FONT color="green">059</FONT>     * @since 3.1<a name="line.59"></a>
<FONT color="green">060</FONT>     */<a name="line.60"></a>
<FONT color="green">061</FONT>    public class DBSCANClusterer&lt;T extends Clusterable&lt;T&gt;&gt; {<a name="line.61"></a>
<FONT color="green">062</FONT>    <a name="line.62"></a>
<FONT color="green">063</FONT>        /** Maximum radius of the neighborhood to be considered. */<a name="line.63"></a>
<FONT color="green">064</FONT>        private final double              eps;<a name="line.64"></a>
<FONT color="green">065</FONT>    <a name="line.65"></a>
<FONT color="green">066</FONT>        /** Minimum number of points needed for a cluster. */<a name="line.66"></a>
<FONT color="green">067</FONT>        private final int                 minPts;<a name="line.67"></a>
<FONT color="green">068</FONT>    <a name="line.68"></a>
<FONT color="green">069</FONT>        /** Status of a point during the clustering process. */<a name="line.69"></a>
<FONT color="green">070</FONT>        private enum PointStatus {<a name="line.70"></a>
<FONT color="green">071</FONT>            /** The point has is considered to be noise. */<a name="line.71"></a>
<FONT color="green">072</FONT>            NOISE,<a name="line.72"></a>
<FONT color="green">073</FONT>            /** The point is already part of a cluster. */<a name="line.73"></a>
<FONT color="green">074</FONT>            PART_OF_CLUSTER<a name="line.74"></a>
<FONT color="green">075</FONT>        }<a name="line.75"></a>
<FONT color="green">076</FONT>    <a name="line.76"></a>
<FONT color="green">077</FONT>        /**<a name="line.77"></a>
<FONT color="green">078</FONT>         * Creates a new instance of a DBSCANClusterer.<a name="line.78"></a>
<FONT color="green">079</FONT>         *<a name="line.79"></a>
<FONT color="green">080</FONT>         * @param eps maximum radius of the neighborhood to be considered<a name="line.80"></a>
<FONT color="green">081</FONT>         * @param minPts minimum number of points needed for a cluster<a name="line.81"></a>
<FONT color="green">082</FONT>         * @throws NotPositiveException if {@code eps &lt; 0.0} or {@code minPts &lt; 0}<a name="line.82"></a>
<FONT color="green">083</FONT>         */<a name="line.83"></a>
<FONT color="green">084</FONT>        public DBSCANClusterer(final double eps, final int minPts)<a name="line.84"></a>
<FONT color="green">085</FONT>            throws NotPositiveException {<a name="line.85"></a>
<FONT color="green">086</FONT>            if (eps &lt; 0.0d) {<a name="line.86"></a>
<FONT color="green">087</FONT>                throw new NotPositiveException(eps);<a name="line.87"></a>
<FONT color="green">088</FONT>            }<a name="line.88"></a>
<FONT color="green">089</FONT>            if (minPts &lt; 0) {<a name="line.89"></a>
<FONT color="green">090</FONT>                throw new NotPositiveException(minPts);<a name="line.90"></a>
<FONT color="green">091</FONT>            }<a name="line.91"></a>
<FONT color="green">092</FONT>            this.eps = eps;<a name="line.92"></a>
<FONT color="green">093</FONT>            this.minPts = minPts;<a name="line.93"></a>
<FONT color="green">094</FONT>        }<a name="line.94"></a>
<FONT color="green">095</FONT>    <a name="line.95"></a>
<FONT color="green">096</FONT>        /**<a name="line.96"></a>
<FONT color="green">097</FONT>         * Returns the maximum radius of the neighborhood to be considered.<a name="line.97"></a>
<FONT color="green">098</FONT>         *<a name="line.98"></a>
<FONT color="green">099</FONT>         * @return maximum radius of the neighborhood<a name="line.99"></a>
<FONT color="green">100</FONT>         */<a name="line.100"></a>
<FONT color="green">101</FONT>        public double getEps() {<a name="line.101"></a>
<FONT color="green">102</FONT>            return eps;<a name="line.102"></a>
<FONT color="green">103</FONT>        }<a name="line.103"></a>
<FONT color="green">104</FONT>    <a name="line.104"></a>
<FONT color="green">105</FONT>        /**<a name="line.105"></a>
<FONT color="green">106</FONT>         * Returns the minimum number of points needed for a cluster.<a name="line.106"></a>
<FONT color="green">107</FONT>         *<a name="line.107"></a>
<FONT color="green">108</FONT>         * @return minimum number of points needed for a cluster<a name="line.108"></a>
<FONT color="green">109</FONT>         */<a name="line.109"></a>
<FONT color="green">110</FONT>        public int getMinPts() {<a name="line.110"></a>
<FONT color="green">111</FONT>            return minPts;<a name="line.111"></a>
<FONT color="green">112</FONT>        }<a name="line.112"></a>
<FONT color="green">113</FONT>    <a name="line.113"></a>
<FONT color="green">114</FONT>        /**<a name="line.114"></a>
<FONT color="green">115</FONT>         * Performs DBSCAN cluster analysis.<a name="line.115"></a>
<FONT color="green">116</FONT>         * &lt;p&gt;<a name="line.116"></a>
<FONT color="green">117</FONT>         * &lt;b&gt;Note:&lt;/b&gt; as DBSCAN is not a centroid-based clustering algorithm, the resulting<a name="line.117"></a>
<FONT color="green">118</FONT>         * {@link Cluster} objects will have no defined center, i.e. {@link Cluster#getCenter()} will<a name="line.118"></a>
<FONT color="green">119</FONT>         * return {@code null}.<a name="line.119"></a>
<FONT color="green">120</FONT>         *<a name="line.120"></a>
<FONT color="green">121</FONT>         * @param points the points to cluster<a name="line.121"></a>
<FONT color="green">122</FONT>         * @return the list of clusters<a name="line.122"></a>
<FONT color="green">123</FONT>         * @throws NullArgumentException if the data points are null<a name="line.123"></a>
<FONT color="green">124</FONT>         */<a name="line.124"></a>
<FONT color="green">125</FONT>        public List&lt;Cluster&lt;T&gt;&gt; cluster(final Collection&lt;T&gt; points) throws NullArgumentException {<a name="line.125"></a>
<FONT color="green">126</FONT>    <a name="line.126"></a>
<FONT color="green">127</FONT>            // sanity checks<a name="line.127"></a>
<FONT color="green">128</FONT>            MathUtils.checkNotNull(points);<a name="line.128"></a>
<FONT color="green">129</FONT>    <a name="line.129"></a>
<FONT color="green">130</FONT>            final List&lt;Cluster&lt;T&gt;&gt; clusters = new ArrayList&lt;Cluster&lt;T&gt;&gt;();<a name="line.130"></a>
<FONT color="green">131</FONT>            final Map&lt;Clusterable&lt;T&gt;, PointStatus&gt; visited = new HashMap&lt;Clusterable&lt;T&gt;, PointStatus&gt;();<a name="line.131"></a>
<FONT color="green">132</FONT>    <a name="line.132"></a>
<FONT color="green">133</FONT>            for (final T point : points) {<a name="line.133"></a>
<FONT color="green">134</FONT>                if (visited.get(point) != null) {<a name="line.134"></a>
<FONT color="green">135</FONT>                    continue;<a name="line.135"></a>
<FONT color="green">136</FONT>                }<a name="line.136"></a>
<FONT color="green">137</FONT>                final List&lt;T&gt; neighbors = getNeighbors(point, points);<a name="line.137"></a>
<FONT color="green">138</FONT>                if (neighbors.size() &gt;= minPts) {<a name="line.138"></a>
<FONT color="green">139</FONT>                    // DBSCAN does not care about center points<a name="line.139"></a>
<FONT color="green">140</FONT>                    final Cluster&lt;T&gt; cluster = new Cluster&lt;T&gt;(null);<a name="line.140"></a>
<FONT color="green">141</FONT>                    clusters.add(expandCluster(cluster, point, neighbors, points, visited));<a name="line.141"></a>
<FONT color="green">142</FONT>                } else {<a name="line.142"></a>
<FONT color="green">143</FONT>                    visited.put(point, PointStatus.NOISE);<a name="line.143"></a>
<FONT color="green">144</FONT>                }<a name="line.144"></a>
<FONT color="green">145</FONT>            }<a name="line.145"></a>
<FONT color="green">146</FONT>    <a name="line.146"></a>
<FONT color="green">147</FONT>            return clusters;<a name="line.147"></a>
<FONT color="green">148</FONT>        }<a name="line.148"></a>
<FONT color="green">149</FONT>    <a name="line.149"></a>
<FONT color="green">150</FONT>        /**<a name="line.150"></a>
<FONT color="green">151</FONT>         * Expands the cluster to include density-reachable items.<a name="line.151"></a>
<FONT color="green">152</FONT>         *<a name="line.152"></a>
<FONT color="green">153</FONT>         * @param cluster Cluster to expand<a name="line.153"></a>
<FONT color="green">154</FONT>         * @param point Point to add to cluster<a name="line.154"></a>
<FONT color="green">155</FONT>         * @param neighbors List of neighbors<a name="line.155"></a>
<FONT color="green">156</FONT>         * @param points the data set<a name="line.156"></a>
<FONT color="green">157</FONT>         * @param visited the set of already visited points<a name="line.157"></a>
<FONT color="green">158</FONT>         * @return the expanded cluster<a name="line.158"></a>
<FONT color="green">159</FONT>         */<a name="line.159"></a>
<FONT color="green">160</FONT>        private Cluster&lt;T&gt; expandCluster(final Cluster&lt;T&gt; cluster,<a name="line.160"></a>
<FONT color="green">161</FONT>                                         final T point,<a name="line.161"></a>
<FONT color="green">162</FONT>                                         final List&lt;T&gt; neighbors,<a name="line.162"></a>
<FONT color="green">163</FONT>                                         final Collection&lt;T&gt; points,<a name="line.163"></a>
<FONT color="green">164</FONT>                                         final Map&lt;Clusterable&lt;T&gt;, PointStatus&gt; visited) {<a name="line.164"></a>
<FONT color="green">165</FONT>            cluster.addPoint(point);<a name="line.165"></a>
<FONT color="green">166</FONT>            visited.put(point, PointStatus.PART_OF_CLUSTER);<a name="line.166"></a>
<FONT color="green">167</FONT>    <a name="line.167"></a>
<FONT color="green">168</FONT>            List&lt;T&gt; seeds = new ArrayList&lt;T&gt;(neighbors);<a name="line.168"></a>
<FONT color="green">169</FONT>            int index = 0;<a name="line.169"></a>
<FONT color="green">170</FONT>            while (index &lt; seeds.size()) {<a name="line.170"></a>
<FONT color="green">171</FONT>                final T current = seeds.get(index);<a name="line.171"></a>
<FONT color="green">172</FONT>                PointStatus pStatus = visited.get(current);<a name="line.172"></a>
<FONT color="green">173</FONT>                // only check non-visited points<a name="line.173"></a>
<FONT color="green">174</FONT>                if (pStatus == null) {<a name="line.174"></a>
<FONT color="green">175</FONT>                    final List&lt;T&gt; currentNeighbors = getNeighbors(current, points);<a name="line.175"></a>
<FONT color="green">176</FONT>                    if (currentNeighbors.size() &gt;= minPts) {<a name="line.176"></a>
<FONT color="green">177</FONT>                        seeds = merge(seeds, currentNeighbors);<a name="line.177"></a>
<FONT color="green">178</FONT>                    }<a name="line.178"></a>
<FONT color="green">179</FONT>                }<a name="line.179"></a>
<FONT color="green">180</FONT>    <a name="line.180"></a>
<FONT color="green">181</FONT>                if (pStatus != PointStatus.PART_OF_CLUSTER) {<a name="line.181"></a>
<FONT color="green">182</FONT>                    visited.put(current, PointStatus.PART_OF_CLUSTER);<a name="line.182"></a>
<FONT color="green">183</FONT>                    cluster.addPoint(current);<a name="line.183"></a>
<FONT color="green">184</FONT>                }<a name="line.184"></a>
<FONT color="green">185</FONT>    <a name="line.185"></a>
<FONT color="green">186</FONT>                index++;<a name="line.186"></a>
<FONT color="green">187</FONT>            }<a name="line.187"></a>
<FONT color="green">188</FONT>            return cluster;<a name="line.188"></a>
<FONT color="green">189</FONT>        }<a name="line.189"></a>
<FONT color="green">190</FONT>    <a name="line.190"></a>
<FONT color="green">191</FONT>        /**<a name="line.191"></a>
<FONT color="green">192</FONT>         * Returns a list of density-reachable neighbors of a {@code point}.<a name="line.192"></a>
<FONT color="green">193</FONT>         *<a name="line.193"></a>
<FONT color="green">194</FONT>         * @param point the point to look for<a name="line.194"></a>
<FONT color="green">195</FONT>         * @param points possible neighbors<a name="line.195"></a>
<FONT color="green">196</FONT>         * @return the List of neighbors<a name="line.196"></a>
<FONT color="green">197</FONT>         */<a name="line.197"></a>
<FONT color="green">198</FONT>        private List&lt;T&gt; getNeighbors(final T point, final Collection&lt;T&gt; points) {<a name="line.198"></a>
<FONT color="green">199</FONT>            final List&lt;T&gt; neighbors = new ArrayList&lt;T&gt;();<a name="line.199"></a>
<FONT color="green">200</FONT>            for (final T neighbor : points) {<a name="line.200"></a>
<FONT color="green">201</FONT>                if (point != neighbor &amp;&amp; neighbor.distanceFrom(point) &lt;= eps) {<a name="line.201"></a>
<FONT color="green">202</FONT>                    neighbors.add(neighbor);<a name="line.202"></a>
<FONT color="green">203</FONT>                }<a name="line.203"></a>
<FONT color="green">204</FONT>            }<a name="line.204"></a>
<FONT color="green">205</FONT>            return neighbors;<a name="line.205"></a>
<FONT color="green">206</FONT>        }<a name="line.206"></a>
<FONT color="green">207</FONT>    <a name="line.207"></a>
<FONT color="green">208</FONT>        /**<a name="line.208"></a>
<FONT color="green">209</FONT>         * Merges two lists together.<a name="line.209"></a>
<FONT color="green">210</FONT>         *<a name="line.210"></a>
<FONT color="green">211</FONT>         * @param one first list<a name="line.211"></a>
<FONT color="green">212</FONT>         * @param two second list<a name="line.212"></a>
<FONT color="green">213</FONT>         * @return merged lists<a name="line.213"></a>
<FONT color="green">214</FONT>         */<a name="line.214"></a>
<FONT color="green">215</FONT>        private List&lt;T&gt; merge(final List&lt;T&gt; one, final List&lt;T&gt; two) {<a name="line.215"></a>
<FONT color="green">216</FONT>            final Set&lt;T&gt; oneSet = new HashSet&lt;T&gt;(one);<a name="line.216"></a>
<FONT color="green">217</FONT>            for (T item : two) {<a name="line.217"></a>
<FONT color="green">218</FONT>                if (!oneSet.contains(item)) {<a name="line.218"></a>
<FONT color="green">219</FONT>                    one.add(item);<a name="line.219"></a>
<FONT color="green">220</FONT>                }<a name="line.220"></a>
<FONT color="green">221</FONT>            }<a name="line.221"></a>
<FONT color="green">222</FONT>            return one;<a name="line.222"></a>
<FONT color="green">223</FONT>        }<a name="line.223"></a>
<FONT color="green">224</FONT>    }<a name="line.224"></a>




























































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